Problem: What do the following two equations represent? $3x-4y = -1$ $9x-12y = 5$
Answer: Putting the first equation in $y = mx + b$ form gives: $3x-4y = -1$ $-4y = -3x-1$ $y = \dfrac{3}{4}x + \dfrac{1}{4}$ Putting the second equation in $y = mx + b$ form gives: $9x-12y = 5$ $-12y = -9x+5$ $y = \dfrac{3}{4}x - \dfrac{5}{12}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.